Most "the sensor reads noise when the motor runs" problems are grounding and layout problems, not sensor problems. A few rules prevent nearly all of them.
Current returns through the ground — that is the whole issue
Ground is not a magic zero-volt reference; it is a conductor with resistance and inductance. When a motor dumps amps through a shared ground trace, that trace develops a voltage — and your sensor's "ground" is now several millivolts (or volts) away from the ADC's. That difference lands directly on your reading. This is a ground loop.
A 100 mm length of ground wire has about 0.001 Ω of resistance and 100 nH of inductance. At what frequency does the inductance matter more than the resistance?
ωL equals R when f = R/(2πL) = 0.001/(2π×100 nH) ≈ 1.6 kHz. Above that the wire is an inductor, and by 10 MHz it is about 6 Ω — four thousand times its DC resistance. This is why "ground" stops being a single node almost immediately: every return path has impedance, that impedance rises with frequency, and any current sharing a path with a sensitive signal turns into a voltage in series with it. It is also why a thicker ground wire barely helps (it changes R, not L) while a shorter one helps a lot.
Try it — a piece of wire is not a short circuit
Star grounding and separate returns
Give noisy loads (motors, solenoids, heaters) their own return path back to the supply, and join everything at one star point — usually at the supply's ground terminal. Never let the motor return current share a trace with analogue signal ground. On a PCB, an unbroken ground plane does this automatically: return current follows the path of least inductance, right under its own signal trace.
Shielding: ground one end only
A cable shield intercepts electric fields and needs a path to ground — but grounded at both ends it becomes a ground loop and carries current, making things worse. For signal cables, ground the shield at one end only, normally the receiver/controller end. For magnetic pickup, shields help little; use a twisted pair so the signal and its return enclose almost no loop area.
Layout habits that just work
Route power and signal cables apart; cross them at 90° if they must meet. Keep loop areas small. Put a decoupling capacitor right at every IC power pin. Add a flyback diode across every relay and solenoid coil — switching an inductor generates a large voltage spike that will reset or destroy nearby electronics. Filter analogue inputs close to the ADC.